CHAPTER 5—EFFECT OF ADVERSE WEATHER

Adverse weather conditions affect the observer by reducing the transmittance of the atmosphere. For example, when light shines through a rainstorm, the raindrops both absorb and scatter the light, thereby reducing the illuminance on an object. During the ENV visual performance experiments, the performance of the VESs in adverse weather conditions was tested for rain, snow, and fog conditions. The results of these investigations are documented in Volumes IV, V, and VI of this report series.

The characterization of the objects in adverse weather conditions was considered as part of this investigation. To account for the effect of the weather conditions on the photometric measures, the transmittance of the atmosphere must be accounted for. From the transmittance, a factor is then used to scale the measured illuminance and luminance values used in the analysis. The method used for calculating the transmittance of the rain, snow, and fog used during the visual performance experiments varies by the weather type. The effect on the photometric characteristics of each of these conditions is considered individually along with their relationship to the visual performance study data.

The rain condition was simulated on the Smart Road using the all-weather testing capabilities at the facility. The capabilities consist of 75 weather-making towers located along the side of the road. The system is operated from a pumping station where the pressure and the rain rate can be controlled to achieve the rain condition desired for the experiment. The rain rate for the object characterization was matched to that of the rain condition experiment.

As mentioned, to investigate the effect of the rain on the object visibility, the transmittance of light through the rain was measured. The transmittance was calculated using ratios of both the luminance and the illuminance under clear and rain conditions, which are shown in figure 69 and figure 70. In these equations, is the atmospheric transmittance, L is object luminance, and E is illuminance on an object. The transmittance of the atmosphere in the rain was then used to scale the object luminance and the background luminance to achieve the resulting contrast and VL in the rain event. It should be noted that the rain transmittance was only measured at one distance (200 ft). In a typical analysis, transmittance would be measured at more than one distance; however, due to difficulties with rain consistency during the characterization process, this was not possible. The 200 ft distance was chosen as it represented close to the mean of the visibility distances found in the other ENV studies (ENV Volume IV).

Figure 69. Equation. Transmittance of illuminance based on the ratio of the clear measurements.

Figure 70. Equation. Transmittance of luminance based on the ratio of the clear measurements.

In the rain event at station 4, measurements were made 61.0 m (200 ft) from the white-clothed parallel pedestrian and the white-clothed perpendicular pedestrian for the HID, three UV–A + HID, five UV–A + HID, HLB, and hybrid UV–A + HLB VESs. The illuminance, object luminance, and background luminance were all evaluated from this location, and then used to calculate the atmospheric transmittance. This calculation was made for each measurement type. The results are shown in figure 71.

All measurements taken from a distance of 61.0 m (200 ft).

Figure 71. Bar graph. Transmissivity of the atmosphere for the illuminance, object luminance, and background luminance in the rain.

It was expected that the transmittance calculated from the illuminance, the object luminance, and the background luminance would be the same; however, this was not the case. It should be remembered that the illuminance measurement was made at the object, meaning that the measured light traveled through the rain only once, whereas the object luminance is effectively attenuated twice as the light travels from the headlamps through the rain to the object and then back through the rain to the photometer. This would result in the effective transmittance being less for the object luminance than the illuminance. For the background luminance, the light traveled through the rain twice, but the background luminance is also influenced by backscatter, which is the light that reflects off the rain. This may have influenced the measurement results. Similarly, the rain was limited to the roadway area, and the viewed background may have been in the roadway or off to the edges, meaning that the entire path of the light was not necessarily within the rain event, and the attenuation from rain did not completely affect the measurement.

These values were used to scale the photometric measurements for comparison to the visual performance results.

The same formulas for the transmittance of the atmosphere that were used for the rain are applicable to the snow conditions. Snow for the investigation was created using the same weather-making system as was used to make the rain, but the ambient temperature was such that the liquid crystallized. For the object characterization measurements, a snow condition was established on the roadway. The original measurement plan was the same as that of the rain; however, it was found that the luminance measurements could not be made reliably because the snow-making action caused the snow to blow. It was then decided that the transmittance of the light through the snow could only be calculated using the measurements of illuminance.

The illuminance measurements were made through the snow for the HID and the HLB VESs at 15.2 m (50 ft), 30.5 m (100 ft), 45.7 m (150 ft), 70.0 m (200 ft), 76.2 m (250 ft), and 91.4 m (300 ft). Multiple distances were used to evaluate the effect of a longer light path through the snow. The illuminance results for the clear and the snow conditions are shown in figure 72. An interesting and unexpected result was the increase in the illuminance value on the object at 15.2 m (50 ft) in the snow condition as compared to the clear condition. This could be caused by light scattering as it passes through the snow. Some of this scatter will be backscatter, which reflects back at the driver, and some will be forward scatter, which scatters onto the object. It is believed the forward scatter causes the observed increase in the illuminance. The effects of the forward scatter and the backscatter were not accounted for in the snow condition experiment, and therefore, cannot be accounted for here.

1 ft = 0.305 m

Figure 72. Line graph. Illuminance for both clear and snow conditions.

The transmittance was calculated for the snow condition for all of the distances with the exception of the 15.2-m (50-ft) distance, and the results are shown in figure 73. As expected, the attenuation of the light increases the farther the measurement is from the vehicle headlamps. An interesting comparison is that of the 45.7-m (150-ft) measurement to the 91.4-m (300-ft) measurement. The transmittance in the snow at 45.7 m (150 ft) is approximately 26 percent and approximately 5 percent at 91.4 m (300 ft). These values are similar to the values at 70.0 m (200 ft) for the illuminance and the object luminance factors in the rain condition, respectively, and further reinforce the hypothesis that the lower value of transmittance for object luminance is due to the impact of the path length through which the light must pass.

1 ft = 0.305 m

Figure 73. Line graph. Transmissivity of the atmosphere for the illuminance through the snow.

As with the rain condition, the calculated values of transmittance through snow were used to scale the photometric measurements for comparison to the visual performance results in the snow condition experiments.

For the ENV studies, fog was manufactured on the Smart Road using the weather-making system. In this configuration, the water was mixed with compressed air in an atomizing nozzle mounted over the center of the roadway. This atomized moisture was then directed to the roadway as fog. The thickness of the fog could be controlled by adjusting the ratio of water to air pressure supplied to the atomizing nozzle.

In fog, light is scattered as a result of the collision of the photons with the water droplets that make up the fog bank. Because of the complexity of this function, a mathematical model of the transmittance was developed to account for the effect of this weather condition. During the fog condition experiments, an illuminance meter was used to measure the backscatter from the vehicle headlamps as a measure of the fog density. These values were then calibrated during the development of the mathematical model. Following is a description of the model development.

When an incident beam of light strikes a particle, the photons, which are much smaller than the particle, are scattered in all directions (figure 74).

Figure 74. Diagram. Possible reaction of light after collision with a water particle in a fog bank.

The exact nature of the scatter pattern depends on many things: the size of the particle, the number of particles, and the polarization of the incident light among others.

A model of this scattering behavior is based on a process called Mie scattering, named after the investigator who developed the foundation of the descriptive model. Mie scattering requires that the scattering particle be larger than the wavelength of the light that is striking it. For a fog bank, the particle sizes range from 0.1 micrometers (µm) to approximately 15 µm.(5) In the case of visible light, the wavelength is in the range of 360 to 800 nanometers (nm), which is much smaller than a typical particle in a fog bank, meaning that the Mie scattering model is valid in the fog scenario.

The nature of the scattering is defined by the angular scattering coefficient (). The symbol represents the angle of observation, measured from the incident ray. By convention, = 0° is in the direction of the incident beam, and = 180° opposes the beam as backscatter. The intensity of the light in the given direction is defined by the equation shown in figure 75, where Eincident is the incident illuminance on the scattering particle.

Figure 75. Equation. Intensity of light based on the scattering coefficient and incident illuminance.

The derivation of () is based on two complex functions (i1, i2), which have particle size, number of particles, observation angle, and index of refraction as parameters. Each of the complex functions represents the nature of perpendicular and parallel polarization. For a headlamp situation, some assumptions can be made that simplify the calculation. The first is that polarization is not an issue because the light source is incoherent (contains many different polarizations and wavelengths). Second, the observation angles for the objects in the roadway environment do not change significantly.

With these simplifications, the total scattering coefficient can be used to quantify the fog characteristic. The total scattering coefficient represents the amount of luminous flux scattered or attenuated from the incident beam. That is to say, as photons are either scattered or absorbed by the particles in the atmosphere, they are removed from the total flux in the incident light beam. To calculate the total scattering coefficient, the incident beam can be broken into very small lamina as shown in figure 76.

Figure 76. Diagram. Depiction of the incident beam broken down into small lamina.

The change in luminous intensity for each lamina can be calculated as shown in figure 77.

Figure 77. Equation. Differential change in illuminance for each portion of a light beam.

Here, the E value is the illuminance incident on the lamina, dx is length of the lamina, and represents the total scattering per unit length. To find the total attenuation for the beam at distance x, the equation in figure 77 must be integrated, yielding the equation in figure 78. This is known as Bouguer’s law of attenuation.

Figure 78. Equation. Total attenuation according to Bouguer’s law.

The visibility of an object is based on the contrast of the object to its background. Because contrast is proportional to the luminance of the target, the contrast can be substituted for the illuminance to represent the reduction in contrast of an object in the fog condition as shown in figure 79.

Figure 79. Equation. Reduction caused by the fog attenuation.

Two assumptions are made during this contrast equation development: that the luminance of the background does not change because of the fog and that the fog is not so significant that it represents the background. In reality though, the light scattered from the fog bank does become the background luminance for the object.

During the calibration procedure, a series of different fog densities were used to generate a scattering field. These densities were developed using varying water pressures at the rain tower base. Each of the VES vehicles in the test was placed in the fog bank, and then a measurement was made of the backscatter from the fog as well as the illuminance provided by the headlamps at distances of 30.48 m (100 ft), 60.96 m (200 ft), and 91.44 m (300 ft). A final measurement was made of the headlamp illuminance and the backscatter in a clear condition without fog. It should be remembered that the measurement of ambient illuminance at the approximate position of the driver’s eye was used as the measurement of backscatter. Table 13 summarizes the measurement matrix used during the calibration procedure.

Using Bouguer’s law, the scattering coefficient was calculated. In this case, the illuminance in the clear condition at each distance was used as Eo. Figure 80 shows the results of the variable.

Figure 80. Scatter plot. Measured backscatter versus the () function.

The extinction ratio, which is the ratio of the clear illuminance to the fog illuminance, was also calculated for each of the vehicles and fog conditions. The results for this calculation are shown in figure 81.

The difficulty with Bouguer’s law is that distance is intrinsically part of the calculation. During the ENV experimentation, visibility distance is the measured value. This means that a relationship exists in the data between the model and the results. In an effort to investigate this relationship, a model of both the total scattering and the extinction ratio was developed. It should be noted that the removal of distance from the equation results in a much more variable equation with a lesser degree of correlation.

The models were developed in two stages. The first stage adjusted all of the vehicle-specific data by the base backscatter illuminance value, obtained from the measured backscatter in the clear condition mentioned as Eo earlier. This value is shown for each of the vehicles in table 14.

Table 14. Backscatter measurements in the clear condition.

Vehicle

Base Backscatter Value

HLB (SUV 1 and SUV 2)

0.06

HID

0.21

HLB–LP

0.15

After adjusting the backscatter model, a single mathematical relation for each of the two variables was developed using a nonlinear regression methodology. The resulting relationships are shown in figure 82 and figure 83. The factor a in the equations is related to the base backscatter value as above.

Figure 82. Equation. () function based on the adjusted backscatter.

Figure 83. Equation. Extinction factor based on the adjusted backscatter.

Each of these models was then used to calculate a metric for the fog density based on the backscatter measurement from each vehicle (figure 84 and figure 85).

Figure 84. Scatter plot. Backscatter versus as per model.

Figure 85. Scatter plot. Backscatter versus extinction with model.

These mathematical models were used with the measured backscatter illuminance measurements to estimate the atmospheric transmittance, and thus, the photometric condition of the objects during the fog condition experiment.

Similar analyses to those performed for the clear condition were performed for the rain, snow, and fog conditions. The correlation of the metrics discussed and the performance of the participants was investigated along with the threshold values for each of the metrics involved.

The correlation analysis for each of the weather conditions are shown in table 15. The dosage factor has also been included in this analysis. In these results it can be seen that there are very similar correlations for the conditions of rain and snow as compared to the clear condition; however, the correlation of the fog condition results for VL to the participant data is less significant.

The results for the recognition distance are very similar, as seen in table 16. Here again the correlation to the fog condition is the lowest of all of the weather conditions, with the VL performing very poorly.

The likely reason why the correlation to the fog conditions is poor is that the changes in the background luminance were not fully accounted for. In the investigation, the luminance of the objects in the fog could not be measured; so instead, they were calculated based on a model of the light extinction. The transmittance model performs well and is well calibrated; however, it does not account for the changes in the visual background of the object. The fog extinguishes the background luminance, but because of scatter, the atmosphere is transformed into a luminous source and becomes the effective background of the object. The effect of this transition was not accounted for in the calculations, likely leading to the poor correlation performance of the photometric values. This problem would not be evident in the other conditions because the rain, while extinguishing the light, does not create a background. Similarly, the snow can become a scattered background, but it would not have the density of fog. It is likely that a complete luminance measurement in all conditions would further aid in this analysis; however, the transient nature of the weather conditions makes it difficult to provide reliable results.

The threshold analysis was performed for the all of the conditions. One of the limitations of this threshold analysis is that no data below the 70-m (200-ft) limit of the photometric measurements could be used. This limitation meant that very little data was available for the calculation for the snow and fog thresholds, so these conditions could not be included in the analysis; however, for the rain condition the threshold results could be considered. In the rain condition, both black-clothed and white-clothed objects were presented, but, as in the snow and fog conditions, very few of the black-clothed conditions met the minimum 70-m (200-ft) criterion, meaning that the threshold for only the white-clothed objects will be presented here.

Figure 86 shows the threshold results for the Weber ratio in the rain condition. This figure shows a very consistent result across all of the VES types and pedestrian locations. It is also interesting to note that the value of this ratio is higher in these conditions than in the clear condition.

Figure 87 shows the threshold results for the VL in the rain condition. These results are less consistent than those for the Weber ratio; however, within the VES base-lamp type, there is some consistency. For example, all of the HLB-based VESs appear to result in a common level of threshold value. In figure 87, as with the Weber ratio, the VL is much higher than that for the clear condition. Where the VL ranged from 40 to 50 for the white-clothed pedestrians in the clear condition, this value is more likely 100 to 150 in the rain condition.

Finally, the threshold dosage for the rain condition is shown in figure 88. This value shows a very consistent result for all of the conditions, particularly within the VES base-lamp types. The HHB seems to require a higher dosage than the other VES types, which might be related to the different aiming location specified for the HHB as compared to the other VESs. As a final note, the dosage level is again higher than that for the clear condition objects.

Each of these metrics shows that a higher threshold value is required in the rain than in the clear condition at the point of detection. This can indicate that the distraction of the driver by the rain event, the attenuation of the light by the rain, and the additional workload of driving in rain require a higher level of lighting to achieve object detection. It should be noted that these calculations are limited because they are based on an attenuation calculation, not direct measurement, and that, as with the clear condition measurement, motion of the object is not taken into account.